Brownian Motion Of Particles Research Articles

Quantifying Brownian motion in the presence of simple shear flow with particle diffusometry.

Particle diffusometry, a technology derived from particle image velocimetry, quantifies the Brownian motion of particles suspended in a quiescent solution by computing the diffusion coefficient. Particle diffusometry has been used for pathogen detection by measuring the change in solution viscosity due to amplified DNA from a specific gene target. However, particle diffusometry fails to calculate accurate measurements at elevated temperatures and fluid flow. Therefore, these two current limitations hinder the potential application where particle diffusometry can further be used. In this work, we expanded the usability of particle diffusometry to be applied to fluid samples with simple shear flow and at various temperatures. A range of diffusion coefficient videos is created to simulate the Brownian motion of particles under flow and temperature conditions. Our updated particle diffusometry analysis forms a correction equation under three different polynomial degrees of shear flow with varying flow rates and temperatures between 25 and 65°C. An experiment in a channel with a rectangular cross section using a syringe pump to generate a constant flow is done to analyze the modified algorithm. In simulation analysis, the modified algorithm successfully computes the diffusion coefficients with 10% error for an average flow rate of up to 8 on all three flow types. Complementary experiments confirm the simulation results.

Convection Confounds Measurements of Osmophoresis for Lipid Vesicles in Solute Gradients.

Lipid vesicles immersed in solute gradients are predicted to migrate from regions of high to low solute concentration due to osmotic flows induced across their semipermeable membranes. This process─known as osmophoresis─is potentially relevant to biological processes such as vesicle trafficking and cell migration; however, there exist significant discrepancies (several orders of magnitude) between experimental observations and theoretical predictions for the vesicle speed. Here, we seek to reconcile predictions of osmophoresis with observations of vesicle motion in osmotic gradients. We prepare quasi-steady solute gradients in a microfluidic chamber using density-matched solutions of sucrose and glucose to eliminate buoyancy-driven flows. We quantify the motions of giant DLPC vesicles and Brownian tracer particles in such gradients using Bayesian analysis of particle tracking data. Despite efforts to mitigate convective flows, we observe directed motion of both lipid vesicles and tracer particles in a common direction at comparable speeds of order 10 nm/s. These observations are not inconsistent with models of osmophoresis, which predict slower motion at ca. 1 nm/s; however, experimental uncertainty and the confounding effects of fluid convection prohibit a quantitative comparison. In contrast to previous reports, we find no evidence for anomalously fast osmophoresis of lipid vesicles when fluid convection is mitigated and quantified. We discuss strategies for enhancing the speed of osmophoresis using high permeability membranes and geometric confinement.

Characterizing rheological properties and microstructure of thioester networks during degradation.

Covalent adaptable networks are designed for applications including cell and drug delivery and tissue regeneration. These applications require network degradation at physiological conditions and on a physiological timescale with microstructures that can: (1) support, protect and deliver encapsulated cells or molecules and (2) provide structure to surrounding tissue. Due to this, the evolving microstructure and rheological properties during scaffold degradation must be characterized. In this work, we characterize degradation of covalent adaptable poly(ethylene glycol) (PEG)-thioester networks with different amounts of excess thiol. Networks are formed between PEG-thiol and PEG-thioester norbornene using photopolymerization. These networks are adaptable because of a thioester exchange reaction that takes place in the presence of excess thiol. We measure degradation of PEG-thioester networks with L-cysteine using multiple particle tracking microrheology (MPT). MPT measures the Brownian motion of fluorescent probe particles embedded in a material and relates this motion to rheological properties. Using time-cure superposition (TCS), we characterize the microstructure of these networks at the gel-sol phase transition by calculating the critical relaxation exponent, n, for each network with different amounts of excess thiol. Based on the measured n values, networks formed with 0% and 50% excess thiol are tightly cross-linked and elastic in nature. While networks formed with 100% excess are similar to ideal, percolated networks, which have equal viscous and elastic components. MPT measurements during degradation of these networks also measure a non-monotonic increase in probe motility. We hypothesize that this is network rearrangement near the phase transition. We then measure macroscopic material properties including the equilibrium modulus and stress relaxation. We measure a trend in bulk network properties that agrees with the values of n. Elastic modulus and stress relaxation measurements show that networks with 50% excess thiol are more elastic compared to the other two networks. As the amount of excess thiol is increased from 0% to 50%, the networks become more elastic. Further increasing excess thiol to 100% reduces the elastically effective cross-links. We hypothesize that these properties are due to network non-idealities, resulting in networks with 50% excess thiol that are more elastic. This work characterizes dynamic rheological properties during degradation, which mimics processes that could occur during implantation. This work provides information that can be used in the future design of implantable materials enabling both the rheological properties and timescale of degradation to be specified.

Ionic current driven by a viscosity gradient.

Gradients of voltage, pressure, temperature, and salinity can transport objects in micro- and nanofluidic systems by well-known mechanisms. This paper explores the dynamics of particles in a viscosity gradient with numerical simulations. The different stochastic rules used to integrate the random motion of Brownian particles affect the steady-state distribution of particles in a diffusivity gradient. Importantly, the simulations illuminate the important role that the boundary conditions play, disallowing a steady-state flux when the boundary conditions mimic those of a closed container, but allowing flux when they mimic electrodes. These results provide an interpretation for measurements of a steady ionic current flowing between electrodes separated by a nanofluidic channel with a liquid viscosity gradient.

Time‐dependent viscosity of structured clay suspensions

AbstractTime‐dependent viscosity of structured clay suspensions under a fixed shear was revealed in the prepared slurry samples of clay lenses from the Athabasca oil sands deposit, differing from thixotropic or rheopectic suspensions. At a lower salt (Na or Ca) concentration, the viscosity oscillated with time, which was slowly damped with increasing salt concentrations. The viscosity increased without reaching a maximum plateau, even after a run of a few hours. At 1000 ppm Na concentration, a maximum viscosity was reached, followed by viscosity fluctuation within a narrow range to approach an equilibrium value with time. Both sample ageing and shear history affected the slurry viscosity. It was speculated that the Brownian motion of colloidal clay particles and the applied shear induced rearrangement and continued formation of clay microstructures with time, due to the rotation of anisotropic colloidal clay particles under simple shear flow. Its implications to oil sands research and operation were briefly discussed.

Force-dependent Fluxes of Adiabatic Classical and Quantum Rocking Ratchets

We consider the adiabatic mode of Brownian particle motion in a periodic potential under the action of symmetric dichotomous fluctuations of an external force F with zero mean value (rocking ratchet), in which the fluctuation frequency is much less than the inverse relaxation time of the particle in each of the states of the dichotomous process. Expressions are given for force-dependent fluxes of an adiabatic classical rocking ratchet. In the absence of thermal fluctuations, within the semiclassical approximation, analytical expressions are obtained for the rocking-ratchet tunneling flux in a sawtooth periodic potential of arbitrary asymmetry and in the potential of two sinusoids. It is shown that the tunneling flux has a linear asymptotics in modulus of small F due to (i) the absence of reverse tunneling fluxes with respect to the direction F and (ii) the root dependence of the integrand of the Gamow formula on the potential energy. The main parameters of the model are the energy barrier V0 and the period L of the potentials, as well as the rocking force F and the asymmetry parameter ξ = l / L of the sawtooth potential with the width of one of its teeth equal to l. It is shown that the direction of quantum ratchet motion is opposite to the motion direction of the corresponding classical ratchet in a limited range of values of the rocking force |F| L / V0 < αc , where the parameter αc changes from the value α1 = (√5 − 1) / 2 ≈ 0.618 for the extremely asymmetric sawtooth potential (ξ = 1) to the value α2 = 2 / 3 ≈ 0.667 for the symmetric potential (ξ= 1 / 2). In the range of values α2 < αc < α2, the sign of the tunneling flux changes with the change in the asymmetry parameter ξ. Numerical calculations for the potential of two sinusoids corresponding to the effective value ξ ≈ 0.655 of the asymmetry lead to similar results with αc ≈ 0.81.

Application of deep learning neural networks for the analysis of fluid-particle dynamics in fibrous filters

A novel hybrid data-driven framework was introduced in this study for the prediction of fluid-particle dynamics of submicron particles under hydrodynamic and Brownian forces in fibrous filters. The distribution of flow parameters was predicted by a high-resolution flow surrogate model based on a deep convolutional neural network (CNN) coupled with a Lagrangian particle tracking method based on the discrete phase model (DPM). The CNN-DPM model was applied to a group of several nonuniformly distributed fibers to calculate filtration efficiency. For CNN training, ground-truth data were obtained using a two-dimensional computational fluid dynamics (CFD) model for laminar incompressible flow. A simulation speedup of three orders of magnitude was obtained by CNN for predicting the velocity components and static pressure distribution within an error range of ±10%. The generalizability of CNN model was also confirmed for overlapped irregular fiber shapes and porosities out of the range of the training dataset with deviations in a range of ±20% in comparison with CFD results. The collection efficiency by CNN-DPM for small particle diameters with dp≤0.3μm was overestimated by approximately 3 % while agreeing well with CFD-DPM for larger particles. The errors of flow velocity predictions by CNN near the fibers added more randomness to the particle motion which was combined with the random Brownian motion of particles, consequently increasing the probability of the small particle hit number and filtration efficiency. The overall acceptable accuracy of the CNN-DPM was confirmed, which is suitable for fibrous filter design and optimization purposes that require thousands of simulations.

Rheological behavior and drying characteristics of ceria-based suspensions under various pH conditions

Microstructural changes in ceria-based suspensions at different pH values and corresponding rheological and drying properties were correlated. Ceria-based suspensions were classified into four zones based on their pH values. Well-dispersed or aggregated states of ceria particles in suspensions were mainly discerned by the magnitude of zeta-potential with pH variations and additional condensation reaction at relatively high pH. Suspensions with well-dispersed particles in a particular pH range exhibited transition between shear-thinning and Newtonian behavior along the shear rate and weak thixotropic features, whereas suspensions with agglomerated particles in different pH ranges showed significant shear-thinning and thixotropic behaviors with shear rate. The motion of particles within suspension droplets in each zone was quantified in terms of autocorrelation functions during drying using multi-speckle diffusing wave spectroscopy. Suspension droplets with well-dispersed particles showed conspicuous coffee-ring patterns compared to those with aggregated particles, owing to the rapid Brownian motion of well-dispersed particles. • The dispersion state of ceria particles depends on the pH condition. • A densely packed structure at high pH originates from the condensation reaction • Rheological properties and drying characteristics are correlated with the microstructures.

Long-time Tails in Quantum Brownian Motion of a charged particle in a magnetic field

We analyse the long-time tails of a charged quantum Brownian particle in a harmonic potential in the presence of a magnetic field using the Quantum Langevin Equation as a starting point. We analyse the long-time tails in the position-autocorrelation function, position–velocity correlation function and velocity-autocorrelation function. We study these correlations for a Brownian particle coupled to Ohmic and Drude baths, via position coordinate coupling. At finite temperatures we notice a crossover from a power-law to an exponentially decaying behaviour around the thermal time scale ħkBT. We analyse how the appearance of the cyclotron frequency in our study of a charged quantum Brownian particle affects the behaviour of the long time tails and contrast it with the case of a neutral quantum Brownian particle.

Analysis of Brownian Motion by Elementary School Students

To stimulate the intellectual curiosity of elementary school students, we conducted a workshop in distance education aimed at exploring the microscopic world inside a cell. In this workshop, elementary school students motivated to learn more on the subject of science analyzed movies of the Brownian motion of micrometer-sized particles suspended in water, using the open-source software Tracker. These students then performed two-dimensional (2D) random walk experiments using a dice game sheet to examine the physical mechanism of Brownian motion. After the workshop, we conducted a questionnaire-based survey. Many participants answered that the contents were difficult but interesting, suggesting that our workshop was very efficient in stimulating the curiosity of motivated students.

Temperature-controlled focusing of Brownian particles in a channel.

The preferential motion of Brownian particles in a channel with heated or cooled walls was numerically simulated using a direct numerical simulation method, that is, the fluctuating-lattice Boltzmann method. The resulting focusing of Brownian particles on the channel centerline induced by heated walls is the focus of this study. The effects of wall temperature, fluid thermal diffusivity, and particle size and density were considered in terms of both the focusing efficiency and performance of Brownian particles. It was revealed that the particle focusing process follows a quadratic relationship with time at high wall temperatures or a linear relationship at low wall temperatures. For a fixed wall temperature, the focusing efficiency (i.e., how fast the Brownian particles aggregate) is dominated by the Prandtl number, that is, the relative importance of the heat transfer and momentum transfer in the fluid. Meanwhile, the Lewis number, that is, the ratio of the fluid thermal diffusivity to the particle self-diffusivity, controls the focusing performance (i.e., to what extent Brownian particles aggregate). The possible mechanisms behind this are discussed. Finally, the negligible influence of particle density on both the focusing efficiency and performance was revealed.

Multiphysics numerical investigation of photothermal self-driving characteristics of SiO2@Au Janus microparticles for drug delivery

The photothermal self-driving process of Janus microparticles has wide application prospects in the fields of biomedicine. Since silica and gold have good biocompatibility and high photothermal conversion efficiency, the SiO2@Au Janus microparticles are widely used as drug carriers. Based on the multiphysics coupling method, the photothermal self-driving process of SiO2@Au Janus microparticles was investigated, wherein the substrate was SiO2 particles and one side of the particles was coated with gold film. Under a continuous wave laser with irradiation of 20 W/cm2, the distance covered by the Janus particles was increased by increasing the thickness of the gold film and reducing the size of the SiO2 particles; the self-driving characteristics of the Janus particles were controlled substantially by increasing the intensity of the incident laser. Based on the simulation results, the thermophoretic motion and Brownian motion of particles can be measured by comparing the absolute values of the thermophoretic force impulse, Brownian force impulse, and drag force impulse. The Brownian force acting on Janus microparticles under low laser power cannot be ignored. Furthermore, the minimum laser power required for Janus particles to overcome Brownian motion was calculated. The results can effectively guide the design of Janus particles in biomedicine and systematically analyze the mechanism of particle thermophoretic motion during drug delivery.

Quantum Brownian motion of a charged oscillator in a magnetic field coupled to a heat bath through momentum variables

We study the Quantum Brownian motion of a charged particle moving in a harmonic potential in the presence of an uniform external magnetic field and linearly coupled to an Ohmic bath through momentum variables. We analyse the growth of the mean square displacement of the particle in the classical high temperature domain and in the quantum low temperature domain dominated by zero point fluctuations. We also analyse the Position Response Function and the long time tails of various correlation functions. We notice some distinctive features, different from the usual case of a charged quantum Brownian particle in a magnetic field and linearly coupled to an Ohmic bath via position variables.

Stability of a Nonlinear ML-Nonsingular Kernel Fractional Langevin System with Distributed Lags and Integral Control

The fractional Langevin equation has more advantages than its classical equation in representing the random motion of Brownian particles in complex viscoelastic fluid. The Mittag–Leffler (ML) fractional equation without singularity is more accurate and effective than Riemann–Caputo (RC) and Riemann–Liouville (RL) fractional equation in portraying Brownian motion. This paper focuses on a nonlinear ML-fractional Langevin system with distributed lag and integral control. Employing the fixed-point theorem of generalised metric space established by Diaz and Margolis, we built the Hyers–Ulam–Rassias (HUR) stability along with Hyers–Ulam (HU) stability of this ML-fractional Langevin system. Applying our main results and MATLAB software, we have carried out theoretical analysis and numerical simulation on an example. By comparing with the numerical simulation of the corresponding classical Langevin system, it can be seen that the ML-fractional Langevin system can better reflect the stationarity of random particles in the statistical sense.

Brownian motion of charged particle in oblique electric and magnetic fields with frictional anisotropy

The Brownian motion of charged particles in oblique electric and magnetic fields with frictional anisotropy is studied for the first time using the white noise functional approach. We obtain the following exact expressions: velocity-space and configuration-space probability density functions, mean square deviations for velocity and displacement, and diffusion coefficients. We investigate the effect of the frictional interaction parameters, Γx (or Γy), on the trajectory of the mean position, and the diffusion coefficients along the x- and y-directions for different values of electric and magnetic field strength.

Quantum Brownian motion for a particle in analog expanding cosmologies in the presence of disclination

In this paper we study the quantum brownian motion of a scalar point particle in the analog Friedman-Robertson-Walker spacetime in the presence of a disclination, in a condensed matter system. The analog spacetime is obtained as an effective description of a Bose-Einstein condensate in terms of quantum excitations of sound waves, named phonons. The dynamics of the phonons is described by a massless real scalar field whose modes are also subjected to a quasi-periodic condition. In this sense, we find exact solutions for the real scalar field in this scenario and calculate the two-point function which makes possible to analyze the mean squared velocity dispersion of the particle in all directions. We, thus, analyze some interesting particular cases and show some graphs where it is possible to see the consistency of our results.

Characterization of fluid flow and heat transfer of a periodic magnetohydrodynamics nano non‐Newtonian liquid with Arrhenius activation energy and nonlinear radiation

AbstractThe focus of this study is to better understand the boundary layer phenomena of nonlinear radiative nano non‐Newtonian (Casson) fluid flow caused by a stretched periphery with a periodic magnetic field and Arrhenius activation energy. The time‐based controlling equations are translated into a suitable dimensionless form using the explicit finite difference (EFD) approach. However, to make the solution convergent, detailed stability and convergence criteria have been devised. In addition, the oscillatory form of velocity, isothermal, and streamline profiles, as well as the conventional shape of other flow fields are displayed. Using tabular analysis, a correlation between non‐Newtonian and Newtonian fluids has even been demonstrated. When the radiative heat flux is evaluated in a linear pattern rather than a nonlinear one, the Lorentz force has been demonstrated to diminish the flow profiles convincingly. Also, another finding is that when the magnetic factor is considered in the sinusoidal form it is controlling the heat transfer factors of nanofluid substantially. As a chemical reaction requires a high‐temperature mechanism to proceed, the scientific principles of activation energy are evaluated in the inclusion of thermal radiation of nonlinear patterns, and the mass transmission is severely influenced. However, in the presence of nonlinear radiation, the Brownian motion of the Casson fluid particles, as well as the thermophoresis phenomena has effectively elevated the temperature field rather than the linear one. The current study has implications for prostate cancer treatment. Nanoparticles have been used to treat cancer, and magnetic fields have been used to regulate the drug emission of the particles.

Thermal bio-convective transport in biological fluid using two viscosity models

This article models the diffusion process of heat and mass transfer in synovial fluid (SF) which is viscous non-Newtonian and is present in the articular cartilage of the synovial joint. The viscosity of SF is a function of the concentration of hyaluronan (HA) and shear rate. The physicochemical properties of HA and the use of antioxidants is the main motivation for considering Brownian motion and thermophoresis in the synovial liquid. The mathematical models for viscosity depending upon concentration and shear rate dependent are coupled with conservation governing equations. To explore the behavior of material parameters on the lubricant nature of the SF models governing laws are solved. The impacts of parameters on friction between joints are examined which helps to analyze the lubricant nature of SFs. Subsequently, it also noted that, in a quantitative sense, viscosity models (model-I and model-II) behave slightly differently under parametric variation. Brownian motion (BM) of particles for the case of the model-I is higher than that for the case of the model-II. The concentration field decreases by increasing the BM of particles. However, the concentration field increases when thermophoresis effects are increased. It is also found from the simulations that thermophoresis effects for the case of a model-II are stronger than those for the case of model-I. BM of particles is responsible for an increase in the temperature for the case of both models.

Experimental and theoretical investigation of an innovative composite nanofluid for solar energy photothermal conversion and storage

Molten salts play a key role in the heat transfer and thermal energy storage processes of concentrated solar power plants. A novel composite material was prepared in this work by adding micron-sized magnesium particles into Li2CO3-Na2CO3-K2CO3 molten salt, the heat transfer and thermal energy storage properties of the composites were studied experimentally. A stable composite nanofluid can be obtained, and a thermal conductivity of 0.728 W/(m·K) at 973 K with an enhancement of 31% is achieved for the Mg/molten carbonate nanofluid. And the strengthening mechanism of thermal conductivity was revealed by using ab-initio molecular dynamics method. It is found that the main bonding interactions exist between Mg and O atoms at the surface of Mg particles. A compressed ion layer with a more compact and ordered ionic structure is formed around Mg particles, and the Brownian motions of Mg particles lead to the micro-convections of carbonate ions around them. These factors are helpful to the enhancement of thermal conduction with the improved probability and frequency of ion collisions. This work can provide a guidance for further studies and applications on metal/molten salt composites with enhanced heat transfer and thermal energy storage capacity.

Porous Media Microstructure Determines the Diffusion of Active Matter: Experiments and Simulations

Active swimmers are known to accumulate along external boundaries owing to their persistent self-motion, resulting in a significant reduction in their effective mobility through heterogeneous and tortuous materials. The dynamic interplay between the slowdown experienced by the active constituents near boundaries and their long-time diffusivity is critical for understanding and predicting active transport in porous media. In this work, we study the impact of boundary layer accumulation on the effective diffusivity of active matter by analyzing the motion of active Brownian particles in an array of fixed obstacles. We combine Janus particle experiments, Brownian dynamics simulations, and a theoretical analysis based on the Smoluchowski equation. We find that the shape, curvature, and microstructure of the obstacles play a critical role in governing the effective diffusivity of active particles. Indeed, even at dilute packing fractions of obstacles, ϕ = 12%, we observed a 25% reduction in the effective diffusivity of active particles, which is much larger than the hindrance experienced by passive Brownian particles. Our combined experimental and computational results demonstrate a strong coupling between the active force and the porous media microstructure. This work provides a framework to predict and control the transport of active matter in heterogeneous materials.